Landau Damping And Frequency-shift Of Monopole Mode In An Elongated Rubidium Bose-Einstein Condensate

Bose-Einstein condensate (Bose-Einstein condensate, BEC) is a Frontierresearch direction in physics concerned by people in recent years. It provides notonly a macro system to study condensed matter and quantum many-body theory butalso a wide application prospects in the field of atom laser, precision measurement,quantum communication and quantum information processing. The research ofelementary excitations is one of the basic topics in statistical physics and condensedmatter physics, and the collective excitations are the most basic excitation modes inBEC. The inter-particle interaction results in not only energy-level shifts ofcollective excitations (called as frequency-shift) but also the decay of theiramplitudes (called as damping). The collective excitation amplitude of boson gasesin trapped potential decay with time mainly through the mechanics of Landaudamping, that is, a quasi-particle absorbs a collective mode and then generate a newquasi-particle. The precision calculation of Landau damping may be used to explainmany experimental phenomena, test and develop the quantum many-body theory forcondensed matter.Although there exists a lot of studies on the Landau damping of collectiveexcitations in trapped BEC made by many famous laboratories and theoretical groupsin the world, the experimental phenomenon of damping are not yet well understoodtheoretically up to now due to the complexity of research issues. Although thedamping is accompanied by the frequency-shift, the calculation of frequency-shift islacking in study of Landau damping in trapped BECs.The Landau damping and frequency-shift of monopole mode in an elongatedrubidium Bose-Einstein condensate are investigated by using the time-dependentHartree-Fock-Bogiliubov (HFB). Different from previous methods, we consideredthe practical relaxations of elementary excitations and the orthogonal relation amongthem in the application of the energy correction formula. With such approach, weprovide new calculation formula for Landau damping rate and frequency-shift. Inaddition, our previous method of eliminating the divergence in three-mode couplingmatrix elements is also improved by zeroing the kinetic energy at the condensateboundary instead of minimizing the ground-state energy. Based on theseimprovements, both Landau damping rate and frequency-shift of the monopole modeare analytically calculated and their temperature dependence are also discussed. Andall the theoretical results are agree with experimental ones.